Question

Is `f(x)=3x^-2 -3` a function?

Answer 1

We can rewrite `f(x)` as `f(x)=3/x^2-3`. For this equation to be a function, one value of `x` must not give more than one value for `y`, so each `x` value has a unique `y` value. Also, every value for `x` must have a value for `y`.

In this case, each value for `x` has one value for `y`. However, `x!=0` since `f(0)=3/0-3="undefined"`.

So, `f(x)` is not a function.

However, it can be made a function by applying limits or ranges of `x` values, in this case it is a function if `f(x)=3x^-2-3,x!=0`.